[Maxima] Shouryya Ray's equation

[dlakelan]

On 06/01/2012 07:39 AM, Jaime Villate wrote:
> On 05/31/2012 05:22 PM, dlakelan wrote:
>> This is fine as a toy math problem, but the proportionality in real
>> physical problems is not a constant.
> Of course, we are talking about a mathematical problem; namely, an
> analytical method to obtain the solution
> to a system of non-linear ODEs.

Yes which is a great thing to do, absolutely, but I do worry that 
students see these specialized tricks too often and have little sense of 
what a "realistic" model looks like or the trouble needed to get 
information out of it.

> I have not made any experimental measurements and I do not play golf,
> but I would be very surprise if a real-life projectile had a perfectly
> plane trajectory like the ones I model using numerical methods :)

I think most golfers will be surprised by that as well :-) they have 
specialized terms for the common kinds of aerodynamic effects such as 
"slice" and "hook", not to mention the ricochet off the trees ;-)

For the course, I used a range of projectiles from a cannon ball at 
about 6 inches (150mm) diameter to a BB at about 0.177 inches (~4 mm) 
with velocities up to 50 m/s and in fluids including air and water. The 
range of drag coefficient was more substantial, and the course was about 
programming, not differential equations.